2023 Higher Education Society Cup National College Student Mathematical Modeling Question C Automatic Pricing and Replenishment Decision of Vegetable Commodities

In fresh food supermarkets, the shelf life of general vegetable products is relatively short, and the quality deteriorates with the increase of sales time.

Most varieties cannot be resold the next day if they are not sold on that day. Therefore, supermarkets usually make decisions based on the historical sales and demand of each product.

Replenishment will be carried out every day.

Since there are many varieties of vegetables sold in supermarkets with different origins, the purchase and transaction time of vegetables is usually between 3:00 and 3:00 in the morning .

4:00 , for this reason, merchants must make replenishment of various vegetable categories on that day without knowing exactly the specific items and purchase prices.

decision making. The pricing of vegetables generally adopts the "cost-plus pricing" method. Shopping malls and supermarkets usually conduct inspections on goods that have been damaged during transportation or have deteriorated in quality.

Discount sales. Reliable market demand analysis is particularly important for replenishment decisions and pricing decisions. From the demand side, vegetables

There is often a certain correlation between the sales volume of commodities and time; from the supply side, the supply of vegetables varies from April to October .

The month is relatively abundant, and the limitations of supermarket sales space make a reasonable sales mix extremely important.

Appendix 1 gives the product information of six vegetable categories distributed by a supermarket ; Appendix 2 and Appendix 3 respectively give the product information.

Sales details and wholesale price data of each commodity in supermarkets from July 1 , 2020 to June 30 , 2023 ;

Appendix 4 gives the recent loss rate data of each commodity. Please establish a mathematical model to solve the following problems based on the attachment and actual situation.

question:

Question 1: There may be certain correlations between different categories or single products of vegetable commodities. Please analyze the distribution patterns and interrelationships of the sales volume of various vegetable categories and single products.

See appendix for complete information!

To analyze the sales distribution patterns and interrelationships between different vegetable categories or single products, the following relationship judgments can be made:
1. Sales trends of different categories

2. Total sales analysis:

The specific code is as follows, see the appendix for complete information:

3. Correlation analysis:

4. Frequent itemsets:

Question 2 Consider that supermarkets make replenishment plans on a category basis. Please analyze the relationship between the total sales volume of each vegetable category and cost-plus pricing, and give the forecast for each vegetable category in the next week ( July 1-7 , 2023) . The total daily replenishment volume and pricing strategy maximize the profits of supermarkets.

See appendix for complete information!

Use time series analysis and a simple cost-plus pricing method to formulate the total replenishment volume and pricing strategy for the vegetable category in the next week. The following is a detailed explanation of the modeling idea:

Data preparation and preprocessing :
- First, import the necessary libraries and load the DataFrame containing the sales data.
- Convert the sales date column into a datetime object to facilitate subsequent time series analysis.
Define the forecast date range :
- Assume that the forecast date range for the next week is July 1, 2023, to July 7, 2023, create pd.date_rangea date range using .
Cycle through each vegetable category :
- Identify each vegetable category by finding its unique category name.
- Create a time series for each category, summarize sales data by date, and use resamplemethods to convert it into daily sales totals.
- Use an ARIMA model to fit time series data to capture its trend and seasonality.
- Use the ARIMA model forecastto predict sales for the next week.
Develop a replenishment strategy :
- Assuming that each vegetable category has an inventory limit (perhaps the storage capacity of the supermarket), we need to ensure that the replenishment does not exceed this limit.
- Determine daily replenishment quantities by comparing forecast sales to inventory caps.
Develop a pricing strategy :
- Assume a simple cost-plus pricing method, in which the pricing strategy is determined based on the average wholesale price of vegetables and a fixed cost-plus percentage.
- Calculate the cost: average the wholesale prices in the sales data as the cost.
- Calculate pricing: Multiply the cost by the cost markup percentage to arrive at the final pricing.

Question 3 : Because the sales space of vegetable products is limited, the supermarket hopes to further develop a replenishment plan for single products, requiring the total number of single products available for sale to be controlled to 27-33, and the order quantity of each single product meets the minimum display quantity requirement of 2.5 kilograms . . Based on the varieties available for sale from June 24 to June 30, 2023, the single product replenishment volume and pricing strategy on July 1 are given , so as to maximize the profits of supermarkets and supermarkets on the premise of meeting the market demand for various types of vegetable commodities .

See appendix for complete information!

Forecast sales volume :
- For each vegetable category, time series data is first created based on historical sales data in order to predict sales volume.
- Use a time series model (the ARIMA model is used here, other models can be selected according to the actual situation) to fit and predict the sales volume to obtain the sales volume forecast for the next day.
Develop a replenishment strategy :
- To ensure that inventory caps are not exceeded, forecast sales are compared to current inventory caps to determine actual replenishment quantities.
- The inventory limit here can be determined based on the maximum sales volume of each item in historical data.
Develop a pricing strategy :
- Calculate the pricing of vegetables based on the cost-plus pricing method.
Generate results :
- Add the replenishment quantity and pricing strategy of each vegetable category to the result DataFrame for subsequent analysis.
- Output the final replenishment quantity and pricing strategy for supplier implementation.
Constraints :
- For further optimization, constraints can be added, such as the total number of items available for sale being limited to a certain range (27-33 items) and the order quantity of each item meeting the minimum display quantity (2.5 kg). These constraints can be satisfied by adjusting the replenishment quantity.

Question 4 In order to better make replenishment and pricing decisions for vegetable commodities, what other relevant data do supermarkets need to collect? How can these data help solve the above problems? Please give your opinions and reasons.